Preheat oven to 350°F. Grease a small loaf pan with baker's spray (be sure to use a plain oil spray with no flour to make this recipe truly gluten-free).
Place the unbroken eggs in a bowl of warm water to bring them to room temperature, set aside.
Measure out the potato flour using the dip and sweep method or by weight. Sift the flour and baking powder into a mixing bowl. Add the salt and whisk well to combine, set aside.
In the bowl of a stand mixer cream the softened butter on medium speed for 1 minute. If your butter is cold you can bring it to room temperature by microwaving on half power for 20-30 second intervals until soft. Check the butter often to prevent it from melting completely.
Scrape down the sides of the bowl then add the sugar to the butter. Beat for a few seconds to incorporate the sugar then add the vanilla extract. Beat on medium-high for 3 minutes .
Scrape down the sides of the bowl. Remove the eggs from the warm water and add them to the bowl one at a time, mixing on low speed for about 30 seconds after each addition. Be sure to scrape the bowl in between additions.
Add the potato flour mixture in 2-3 batches alternating with the Brandy. Scrape down the sides of the bowl and mix well (about 30-40 seconds) after each addition.
Pour the batter into the prepared pan and smooth with a spatula. Firmly tap the pan on a counter a few times to eliminate any air bubbles. Bake @ 350°F for 40-45 minutes or until a wooden toothpick comes out clean.
Let the cake cool in the pan for 10 minutes, then remove onto a cooling rack.